When you buy a new handgun, it usually comes in a hard plastic box along with a safety cable, ect....?

...occionally when you buy one you also get the box (cardboard) that it was shipped in. On the outside of this box there is usually various information including the company name, model number, ect...my question is that this box sometimes has a serial number somewhere on it. Is this the same serial number that is on the gun, or does the box it's shipped in also have a seperate serial number? Reason I'm asking is that a gun of mine was recently stolen I've misplaced the paper where I had all the serial numbers written down, but I still have the box that the kel tec .380 came in and I'm wondering if the serial numbers are the same.